Concept explainers
To graph: The function and compare that with the standard equation.
Given information:
Graph the function y=−x2−5 and compare it with the graph of y=x2 .
Graph:
The data points to graph the function y=−x2−5 are shown in Table -1. The graphs of the functions y=−x2−5 and y=x2 are shown in Fig. (1).
Step 1: Make a table for values of y=−x2−5 , here Table-1.
Step 2: Plot the points shown in Table-1.
Step 3: Draw smooth curve passing through the table points.
Step 4: Compare the graphs of y=−x2−5 and y=x2 shown in Fig. (1).
(a) The graph of the function y=−x2−5 opens down, while that of function y=x2 opens up.
(b) Both graphs have same axis of symmetry y -axis or line x=0 .
(c) Graph of function y=−x2−5 has vertex at point (0,−5) and the graph of function y=x2 at point (0,0) .
(d) Then distance between the vertices of graph of y=−x2−5 and graph of y=x2 is 5 units.
Interpretation:
The graphs of the quadratic functions are parabolas with axis symmetry x=0 and vertex the point (0,0) .
Chapter 1 Solutions
Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
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